Does your promotion point start over when you get promoted to SGT?

Well, in a sense yes and no. Once you hit the minimum required time for look for SSG, you will have to recalculate your points since they will change but they shouldn't go back down to Zero

Points only show up on our ERB when you’re promotable. Since you just got promoted to SGT, you’re not promotable anymore. Once you become promotable as a SGT, the points will populate again in the promotion points section. At anytime however, you can check and see how many points you have by pulling up your promotion point worksheet on the HRC page. Keep in mind, the points scale for apft and weapons are different for promotion to SGT than those for promotion to SSG. You earn less points for apft and weapons when competing for promotion to SSG.

Have you gone to the HRC website and used the PPW? You will retain certain points but loose other (i.e. points for NCOES) and the point system slightly changes from E5 to E6. However, you will still have promotion points. The reason why you do not see them on your ERB/SRB is due to you are no longer promotable.